How much material will be left if a radioactive isotope has a half life of 1.3 billion years in 3.9 billion years?

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Answer 1 · 2014-07-21T18:47:39

You will have 12.5 % of the parent material after 1.3 billion years.

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Method 1

In your problem, the number of half-lives is

#n# = 3.9 billion years × #(1"half-life")/(1.3"billion years")# = 3.0 half-lives

The amount remaining after 3 half-lives is

100 % × #1/2 × 1/2 ×1/2 = (100"%")/8# = 12.5 %

Method 2

#A=A_0/2^n = (100 %)/2^3.0# = 12.5 %